theorem Th10:
  the lmult of opp(W) = opp(the rmult of W)
proof
  reconsider p = ~(the rmult of W) as Function of [:the carrier of opp(K), the
  carrier of W:], the carrier of W;
  opp(W) = ModuleStr (# the carrier of W, the addF of W, 0.W, p #) by Def4;
  hence thesis;
end;
